[ToikY]

Change and mathematical scope

NO VERIFIED GAIN. The comparator remains #7334 at aaeec8c0acf01e99a5f331ef363a698d9c084ace with signed #7113 at 07a76c5e2738882c0cb322278e56f6cae3c9885d.

For the four paid pairs in #7371, keep both signed ADD clocks, move the selected public role directly from A to C, and retain its peer's path. At each original clock allow the exact cocharted public donor rows and a destination diagonal. The second check uses the literal post-first row. Both independent engines exclude all eight banks over the rationals. Seven have a missing signed coordinate. The remaining bank has the separating covector x1488 − 2x1493, which annihilates its only granted donor and evaluates to −2 on the required signed response. All eight keys were tested, with zero unresolved.

The 17-copy paid price changes rank-one count by −34 and rank-two count by +17 for one edit, and keeps productive positions fixed. The directed one-edit saving upper is 0.08583213854035211 raw, or 0.34332855416140845 across all four if compatible. The quote includes an ordinary ceiling conditional on the stated coefficient/routing gate. The exact span test rules out this family before any build.

Task and overlap

This is task p104-side-correction with the changed scope of two fixed-clock public banks. #7371 moved the ADD pair together. #7355 and #7336 supply earlier donor-span tools and single-source checks. #7338 inventories the same paid pairs under a different virtual-owned construction. The exact R116 public manifest at #7371 is authenticated in this replay.

The research commit adds only research/p104-fixed-clock-two-bank-bound/, with scientific inputs bound to canonical main e54523517d0f03e58352e647c403a5af3e525a57. The two existing #7257 commits are a CI prerequisite for the canonical #7000/#6030 navigation mismatch documented in #7371.

Validation

With CPython 3.12 from a clean checkout:

python3.12 -I -B research/p104-fixed-clock-two-bank-bound/replay.py

The Git-free replay regenerates the full price, both exact bank checks and the signed witness agreement. Altered price and word fail. Registered-package, committed-byte/source-history, navigation and export checks passed. No literal candidate or whole multiplier was constructed in this scope.

Credit and open next questions

#7334 supplies the exact word and #7113 supplies the signed caller. #7371 supplies the four frozen pairs and the endpoint exclusion. #7355/#7336 supply exact donor and reverse-covector methods. OpenAI Codex and subagents materially assisted. The next separate test is a fixed-paid productive split on one of the remaining #7370 endpoint groups, starting with exterior prefix support. Review and merge are left to the maintainers.